The thesis examines diverse methods of damping the librational motion of earth-orbiting satellites. Starting with passive stabilization, two classical mechanisms for energy dissipation are studied, for performance comparison, when executing librations in the orbital plane. The first model, consisting of a sliding mass restricted to relative translational motion with respect to the main satellite body, establishes the suitability of various approaches to the problem in circular orbit. In this case, numerical and analog methods do not readily yield information on the influence of parameters and approximate methods are found to be particularly helpful. Butenin's method based on averaging techniques predicts the response of the satellite with good accuracy for small damping constant while the exact solution to the linearized equations provides optimum damper characteristics for motion in the small. A comparison of the sliding mass damper model with a damper boom mechanism involving only relative rotational displacements, is then performed for equal equilibrium inertias of the damping devices. It indicates that, for optimum transient tuning, the damper boom would have a better time-index while the sliding mass would lead to smaller steady-state amplitudes for low eccentricity orbits. A numerical example using GEOS-A satellite data illustrates the outcome of the study when applied to physical situations. A stability analysis is also included which uses Routh and Lyapunov approaches to determine the domain of parameters leading to asymptotic stability, as well as numerical methods to define the bounds on stable initial disturbances: it is found that for most practical applications, the stability contour in circular orbit is close to that of the undamped case. How-ever, for eccentric trajectory, the amount of damping critically affects asymptotic stability. The next model, which involves active stabilization, uses solar radiation pressure to achieve planar librational control of a satellite orbiting in the plane of the ecliptic. This is obtained by adjusting the position of the center of pressure with respect to the center of mass through a controller depending on a linear combination of librational velocity and displacement. The motion in circular orbit is; first investigated through the W.K.B. method. Although the approximate equation involves an infinity of turning points, only a few of them are required to evaluate the damped behaviour of the system. A comparison of the analytical results with a numerical integration of the exact equation of motion shows good agreement only over a limited range of parameters and, therefore, the latter is used to complete the study for circular and elliptic cases. The concept leads to great versatility in positioning a satellite at any angle with respect to the local vertical. Also, high transient ; performance is observed about local vertical and horizontal and the dichotomous property of good transient associated with poor steady-state inherent to passive damping can be avoided by selecting appropriate controller parameters. An example is included which substantiates the feasibility of the configuration. Finally, the attention is directed towards the influence of gravity torques on the stability of damped axisymmetric dual-spin satellites. The nutation damper mounted on the slowly-spinning section is of the pendulum type. For this section rotating at orbital angular rate, application of the Kelvin-Tait-Chetaev theorem indicates that the asymptotic stability region reduces basically to the mainly positive stable spin region of the undamped case. However, some care is required depending upon the shape and natural frequency of the damper. If the damper section rotates at a much higher rate than the orbital one, torque-free motion need only be considered for short term pre-dictions. Stability charts corresponding to this case, given for comparison, emphasize the effect of gravity. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The feasibility of utilizing the environmental forces for three-axis librational damping and attitude control of spinning satellites is investigated in detail. An appreciation of the environmental influence is first gained through a librational dynamics study of spinning, axisymmetric, cylindrical satellites in the solar radiation pressure field. The highly nonlinear, nonautonomous, coupled equations of motion are analyzed approximately using the method of variation of parameters. The closed form solution proves to be quite useful in locating periodic solutions and resonance characteristics of the system. A numerical parametric analysis, involving large amplitude motion, establishes the effect of the radiation pressure to be substantial and destabilizing. Next, a possibility of utilizing this adverse influence to advantage through judiciously located rotatable control surfaces is explored. A controller configuration for a dual-spin spacecraft is analyzed first. The governing equations, in the absence of a known exact solution, are solved numerically to evaluate the effect of system parameters on the performance of the control system. The available control moments are found to be sufficient to compensate for the rotor spin decay, thus dispensing with the necessity of energy sources maintaining the spin rate. The controller is able to damp extremely severe disturbances in a fraction of an orbit and is capable of imparting arbitrary orientations to a satellite, thus permitting it to undertake diverse missions. The development of an efficient yet structurally simple controller configuration is then considered. A logical approach for solar controller design is proposed which suggests a four-plate configuration. Its performance in conjunction with a bang-bang control law is studied in detail. The utilization of maximum available control moments leads to a substantial improvement of the damping characteristics. Attention is then focussed on using the earth's magnetic field interaction with onboard dipoles for attitude control. Magnetic torquing, however, is unable to provide first order pitch control in near equatorial orbital planes. The shortcoming is overcome by hybridizing the concepts of magnetic and solar control. Two magnetic controller models, employing a single rotatable dipole or two fixed dipoles, are proposed in conjunction with a solar pitch controller. The system performance is evaluated for a wide range of system parameters and initial conditions. Although high spin rates lend considerable gyroscopic stiffness to the spacecraft, the controllers continue to be quite effective even in the absence of any spin. Even with extremely severe disturbances, damping times of the order of a few orbital degrees are attainable. As before, the concept enables a satellite to change the desired attitude in orbit. The effectiveness of the controllers at high altitudes having been established, the next logical step was to extend the analysis to near-earth satellites in free molecular environment. A hybrid control system, using the solar pressure at high altitudes and the aerodynamic forces near perigee, is proposed. The influence of important system parameters on the bang-bang operation of the controller is analyzed. The concept appears to be quite effective in damping the satellite librations. Both the orbit normal and the local vertical orientations of the axis of symmetry of the satellite are attainable. However, for arbitrary pointing of the symmetry axis, small limit cycle oscillation about the desired final orientation results. Finally, the time-optimal control, through solar radiation pressure, of an unsymmetrical satellite executing planar pitch librations is examined analytically. The switching criterion, synthesized for the linear case, is found to be quite accurate even when the system is subjected to large disturbances. Throughout, the semi-passive character of the system promises an increased life-span for a satellite. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

Approved for public release; distribution is unlimited. / NPSAT1 is a gravity-gradient friendly, prolate body designed to fly at 600 Å 40 km inclined to 34.5 degrees. The satellite uses a magnetic 3-axis active attitude control system (ACS) using magnetic torque rods that interact with the Earth's magnetic field. This thesis accomplishes three goals. The first objective was to verify and to validate the magnetic attitude control system program and model developed by Leonard. The verification and validation process was completed in two steps. The first step accomplished an independent modeling of the Earth's magnetic field using MATLAB. The second step completed a verification via inspection of Leonard's ACS SIMULINK model. The verification confirmed that Leonard's modular sub-components of the disturbance torques, the quaternion vectors, the Euler angles, the spacecraft kinematics and dynamics, and the ACS control laws conformed to current ACS empirical theory. The second goal was to establish a laboratory used to demonstrate the ACS robustness and ability to perform as designed. The laboratory was created to house an air-bearing platform that simulates NPSAT1 characteristics. The third goal was to perform hardware-in-the-loop experiments with the NPSAT1 ACS software and model. Hardwarein- the-loop tests were performed to the magnetic torque rods, torque rod driver circuit board, micro-controller computer, and control interfaces. Specifically, solenoid current tests, magnetic field determination tests, and digital-to-analog conversion tests were completed. / Lieutenant Commander, United States Navy

The thesis identifies several limitations in the modelling and attitude stability analysis of two classes of spacecraft: rigid and flexible satellites. Attractive methods are proposed which promise to have far reaching consequences in spacecraft dynamics. These alternatives, developed based on techniques of differential equations, classical mechanics, and differential topology, are indicated below. (a) An Alternate Transition from the Lagrangian of a Satellite to Equations of Motion The classical procedure requires the Lagrangian to be expressed in terms of the corresponding generalized coordinates of the problem. This requirement significantly complicates the derivation of the equations of motion through an introduction of a set of librational generalized coordinates, which is strictly not a part of the dynamical system. Using the Lagrangian in the natural variables (angular velocity, direction cosines, and vibrational coordinates), one develops a procedure for derivation of equations of motion without an a priori choice of rotational generalized coordinates. For the case of a satellite with two flexible plate-type appendages, for example, the approach reduced the formulation time to one-third. (b) Synthesis and Depiction of Rotational Motion of Satellites and Robots The rotational coordinates in use for numerical prediction of orientation of a satellite are either singular or redundant. Furthermore, they lack a convenient visual interpretation. A new set of coordinates is proposed and an associated representation is developed which avoids these limitations. The procedure is applied to represent and integrate numerically the librational response of the flexible satellite mentioned in (a). (c) Resolution of Attitude Stability of Delp Satellites The development here tackles a long outstanding problem in the area of attitude stability of satellites. The resolution of this problem through normalization of the Hamiltonian leads to a better appreciation of stability associated with the class of gravity gradient structures such as the proposed Space Station. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

A wide variety of scientifically interesting missions could be enabled by orbital flight altitudes of 150 – 250 km. For the present work, this range of altitudes is defined as extremely Low Earth Orbit (eLEO). The use of low-cost nanosatellites (mass < 10 kg) has reduced the cost barrier to orbital flight over the last decade and the present study investigates the feasibility of using primarily commercial, off-the-shelf (COTS) hardware to build a nanosat specifically to allow extended mission times in eLEO. CubeSats flying in the lower thermosphere have the potential to enable close monitoring of the Earth’s surface for scientific, commercial, and defense-related missions. The results of this research show that the proper selection of primary and attitude control thrusters combined with precise control techniques result in significant extension of the orbital life of a CubeSat in eLEO, thus allowing detailed explorations of the atmosphere. In this study, the orbit maintenance controller is designed to maintain a mission-averaged, mean altitude of 244 km. An estimate is made of the primary disturbance torque due to aerodynamic drag using a high-fidelity calculation of the rarefied gas drag based on a Direct Simulation, Monte-Carlo simulation. The primary propulsion system consists of a pair of electrospray thrusters providing a combined thrust of 0.12 mN at 1 W. Results of a trade study to select the best attitude control option indicate pulsed plasma thrusters operating at 1 W are preferable to reaction wheels or mangetorquers at the selected altitude. An extended Kalman filter is used for orbital position and spacecraft attitude estimations. The attitude determination system consists of sun sensors, magnetometers, gyroscopes serving as attitude sensors. The mission consists of two phases. In Phase I, a 4U CubeSat is deployed from a 414 km orbit and uses the primary propulsion system to deorbit to an initial altitude within the targeted range of 244 +/- 10 km. Phase I lasts 12.73 days with the propulsion system consuming 5.6 g of propellant to deliver a ∆V of 28.12 m/s. In Phase II the mission is maintained until the remaining 25.2 g of propellant is consumed. Phase II lasts for 30.27 days, corresponding to a ∆V of 57.22 m/s with a mean altitude of 244 km. The mean altitude for an individual orbit over the entire mission was found to vary from a maximum of 252 km to a minimum of 236 km. Using this approach, a primary mission life of 30.27 days could be achieved, compared with 3.1 days without primary propulsion.

The accurate determination of spacecraft attitude has always been a critical issue in many applications. The presence of imperfect sensors introduces errors in the system and affects the outcome of the mission. One of the most significant sensors is the rate gyroscope. Particularly, the rate gyros are known to degrade with time, introducing random noise and bias. This calls for estimation algorithms which process the measured data in order to reduce the effects of the disturbances to a minimum. This research presents an approach which takes full advantage on the nonlinear dynamics and possibly non-Gaussian disturbances. It is based on recent work involving particle filters, where the probability density functions are approximated by a relatively large number of parameters. It is shown that accurate attitude estimation can be obtained with a manageable number of particles.

Approved for public release; distribution is unlimited / Design requirements for a small satellite (NPSAT-1) Attitude Determination and Control Subsystem (ADCS) is a three-axis stabilized spacecraft which requires a control attitude of +/- 1.0 degrees and knowledge attitude of +/- 0.1 degree. Several design aspects are considered in development of attitude control systems for a small satellite, such as: spacecraft dynamics, space environment, disturbance torques, orbit type, and spacecraft complexity. The ideal spacecraft's attitude sensor is a rate gyroscope, which provides rate information to the attitude control system. In the case of NPSAT-1, due to budget constraints alternative sensors will be utilized, such as: a three-axis magnetometer, earth sensors, and a Global Positioning System (GPS). A small satellite designed to have a three-axis stabilized, biased momentum system, must have a robust control system and requires a momentum wheel to provide stiffness to maintain attitude, and magnetic torque rods on each axis. The current design of NPSAT-1 uses all of these sensors to provide rate information for damping and stability to the control system that requires a complicated attitude control design. The purpose of this attitude control design simulation is to investigate and propose a control law utilizing a single pitch momentum wheel and three magnetic torque rods. A further proposal is to utilize a constant speed momentum wheel to avoid momentum damping and over speed, replace the pitch control with magnetic torquers, and develop a Kalman filter estimator to provide all the required angular rates. / Lieutenant Commander, United States Navy

Approved for public release; distribution is unlimited / Design Center of the Naval Postgraduate School. The objective of this simulator is to provide on-the-ground simulation of the dynamics and control of spacecraft for high precision Acquisition, Tracking and Pointing applications associated with space based laser relay. The required initial attitude determination accuracy for the Bifocal Relay Mirror test-bed is 10 æ-radians. Normally, in laboratories where very high initial attitude knowledge is required, actual (space qualified) star trackers are incorporated into the testbed design. This is not possible at NPS as the laboratory does not have a skylight to allow visual access to the stars, and the photosensitive nature of many of the experiments would make such an opening inconvenient. Since it is critical to the operation of the testbed to provide accurate attitude knowledge, a substitute system was required. The present thesis documents the development of a new attitude sensor capable of providing attitude information within the required 10æ-radians (within a field of view of the order of 1 deg). The concepts leading up to the final design, the testing and selection of the equipment used in the final configuration, and a detailed explanation of how the final system calibration was performed are discussed in detail. / Lieutenant, United States Navy

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Thesis (M.S.)--University of Hawaii at Manoa, 2006. / Includes bibliographical references (leaves 92-93). / x, 93 leaves, bound ill. 29 cm